MAT 266 Lecture 6: MAT 266-Lecture 6- 6.2 Trig Integrals and Substitution
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Mat 266 -- lecture 6 6. 2 trig integrals and substitution. Each group shown below are specific techniques to help calculate the following indefinite integrals; Group 1: used for all sin and cos to an odd power** = cos(cid:894)x(cid:895)dx - (cid:1006) sin2(cid:894)x(cid:895)cos(cid:894)x(cid:895)dx + sin4(x)cos(x)dx u=sin(x), du= cos(x)dx. = sin(x) -2/3 u3 + 1/5 u5 + c. = sin(x) 2/3 sin3(x) + 1/5 sin5(x) + c. Group 2: used with the product of sin and cos with at least one of them to an odd power** ***multiply each term, think of it as 2( x + y)z = 2xz +2yz*** = 1/5 sin5(x) 1/7 sin7(x) + c. Group 3: used with sin and cos when it is to an even power** Important trig formulas cos2(x) = + cos (2x) *note: 2x is double the angle of either cos or sin sin2(x) = - sin (2x) Implement the formula from above for each of the cos2(3x)
